Questions: A finance analyst is examining the contributions of three projects on company productivity. Project A represents 10% of resources (with a 50% success rate), Project B represents 30% of resources (with a 60% success rate), and Project C represents 60% of resources (with a 90% success rate). Calculate the weighted average success rate for the company. 58 % 67 % 77 % 54 %

Solution Steps

To calculate the weighted average success rate, we need to multiply the success rate of each project by its respective weight (percentage of resources) and then sum these values. The formula for the weighted average is:

\[ \text{Weighted Average} = (w_1 \times r_1) + (w_2 \times r_2) + (w_3 \times r_3) \]

where \( w_i \) is the weight of project \( i \) and \( r_i \) is the success rate of project \( i \).

We have three projects with the following weights and success rates:

• Project A: \( w_1 = 0.10 \), \( r_1 = 0.50 \)
• Project B: \( w_2 = 0.30 \), \( r_2 = 0.60 \)
• Project C: \( w_3 = 0.60 \), \( r_3 = 0.90 \)

The weighted average success rate is calculated using the formula:

\[ \text{Weighted Average} = (w_1 \times r_1) + (w_2 \times r_2) + (w_3 \times r_3) \]

Substituting the given values:

\[ \text{Weighted Average} = (0.10 \times 0.50) + (0.30 \times 0.60) + (0.60 \times 0.90) \]

\[ = 0.05 + 0.18 + 0.54 = 0.77 \]

Convert the weighted average to a percentage by multiplying by 100:

\[ \text{Weighted Average Percentage} = 0.77 \times 100 = 77.0\% \]

Final Answer